feat(search): Tavily + Brave behind a search-provider port; Google CSE retires

Search port + model slots wave, chunk A (owner design, 2026-09-20):
- core/search.ts: SearchHit + SearchProvider port + SearchStatus —
  pure, browser-safe; adapters arrive as injected dependencies.
- server/search.ts: Tavily + Brave adapters (wire shapes VERIFIED
  against docs.tavily.com's OpenAPI + Brave's dashboard docs — Tavily
  auth is the Bearer header, not the legacy body api_key; Brave is
  X-Subscription-Token) + engine resolution per owner decisions: a key
  ALONE activates its engine (no engine choice needed), explicit
  agent.search.engine pins the preference (both keys: Tavily first),
  a pinned engine with a missing key is honestly unavailable — no
  silent fallback, no default engine.
- Curated keys catalog: GOOGLE_SEARCH_API_KEY/GOOGLE_CSE_ID retire
  (CSE closed to new customers, dies Jan 2027 — stored values become
  preserved unknown vars); TAVILY_API_KEY (tvly- shape) + BRAVE_API_KEY
  (length guard) join. UI keys-section TOOL_IDS now derives from the
  catalog — cannot drift.
- GET /api/search: {available, engine, reason} — the honest status for
  the settings gray-out; researcher-disable semantics ride the same
  signal (Teacher stream rewires the tool onto the port).
- agent.search settings field (schema + sanitizer + strict parser);
  web.ts's WebSearchResult is now the core SearchHit (re-exported).

src/server/settings-body.ts

@@ -184,6 +184,16 @@ export function parseAgentSettingsBody(body: unknown): SettingsBodyResult<AgentS
 	const prompts = parseBooleanMap(raw.prompts, "prompts");
 	if (prompts.error) return { ok: false, error: prompts.error };
 	if (prompts.map) settings.prompts = prompts.map;
+	if (raw.search !== undefined) {
+		const search = asRecord(raw.search);
+		if (!search) return { ok: false, error: "search must be an object" };
+		if (search.engine !== undefined) {
+			if (search.engine !== "tavily" && search.engine !== "brave") {
+				return { ok: false, error: 'search.engine must be "tavily" or "brave"' };
+			}
+			settings.search = { engine: search.engine };
+		}
+	}
 	return { ok: true, settings };
 }